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The theory of path homology for digraphs was developed by AlexanderGrigor'yan, Yong Lin, Yuri Muranov, and Shing-Tung Yau. In this paper, weconsider the differential algebras on digraphs and define the parametrizedhomology of digraphs as an analog of the path homology. We prove thefunctoriality of the parametrized homology of digraphs in Theorem 4.2. We alsoprove some Kunneth-type formulae for the parametrized homology of digraphs inTheorem 4.4.

Differential algebras on digraphs and parametrized homology